Question

Decision Tree

Alligash County does not allow liquor to be sold in restaurants. A referendum will be held in three months in which residents will vote on whether to change the lawand allow liquor to be sold in restaurants. The latest poll estimates that there is a 60% chance that the referendum will pass. A local speculator, Henry Cogswell, isconsidering buying a closed restaurant that is being sold at a sealed bid auction. Henry thinks that a bid of $1.25 million will have a 25% chance of winning, a bid of$1.45 million will have a 45% chance of winning and a bid of $1.85 million will have an 85% chance of winning. (Note that these probabilities do not add to one andthere is no reason they should – they are different bids.) If Henry wins the auction and the referendum passes he thinks he could sell the restaurant for $2.2 millionbut if the referendum does not pass he thinks he will only be able to get $1.15 million for the restaurant. Draw a decision tree for this problem and use it todetermine what Henry should do.

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